A wide variety of different types of adaptive filters are known. These filters include causal filters in which the filter output depends only on past and present inputs, as well as anti-causal filters in which the filter output depends only on future inputs.
In one typical arrangement, adaptive filter coefficients are updated periodically so as to reduce the error between the actual filter output signal and a desired signal or reference signal. This may involve use of a specified adaptive algorithm such as the least mean squares (LMS) algorithm, which attempts to determine filter coefficients that produce the least mean squares of the error signal.
Adaptive filters find application in numerous communication system applications, including, by way of example and without limitation, interference cancellation, linear prediction, and signal identification.
A significant drawback of conventional adaptive filtering arrangements is that in such arrangements it can often be very difficult to adapt the filter coefficients accurately and efficiently under varying operating conditions of the communication system in which those filters are implemented.